I wasn't sure whether to post this in the classical or relativity section. While pondering something I found an embarrassing gap in my knowledge. I can't quite get my head around this problem and I need a fresh perspective. Consider two beams of electrons moving parallel to each other. The electrons are monoenergetic (all moving at exactly the same velocity, v). Each beam, being a flow of charge, carries a current I. Now,in the laboratory rest fram, an observer sees two current carrying streams of particles which will tend to attract each other due to their magnetic field. There would appaer to be a force acting parallel to the direction of motion of the electrons. In the rest frame of an electron in the beam, none of the other electrons are moving, so the electron sees no current and hence, no magnetic field. The only forces are electrostatic. So do the beams attract each other or not? Why does there appear at first glance to be a transverse force which can be transformed away? I'm sure I've made a trivial oversight somewhere. Help.